Question: $h(t) = -3t^{2}$ $f(x) = -x^{3}+7x^{2}+4(h(x))$ $g(x) = -4x^{2}-5x-5-2(h(x))$ $ h(g(4)) = {?} $
Explanation: First, let's solve for the value of the inner function, $g(4)$ . Then we'll know what to plug into the outer function. $g(4) = -4(4^{2})+(-5)(4)-5-2(h(4))$ To solve for the value of $g$ , we need to solve for the value of $h(4)$ $h(4) = -3(4^{2})$ $h(4) = -48$ That means $g(4) = -4(4^{2})+(-5)(4)-5+(-2)(-48)$ $g(4) = 7$ Now we know that $g(4) = 7$ . Let's solve for $h(g(4))$ , which is $h(7)$ $h(7) = -3(7^{2})$ $h(7) = -147$